Aircraft: PREMIER 1
Phase of flight: Landing
Anomaly: Aircraft Equipment Problem Less Severe; Ground Event / Encounter Other / Unknown; Inflight Event / Encounter Weather / Turbulence

The following is my best recollection of the aircraft event at DTO.We were re-dispatched to DTO with [an] the alternate. As always; weather was one of the items discussed as part of the Company dispatch procedure. Once airborne and in range of DTO; based upon the DTO weather; runway conditions; and aircraft performance in consultation with the Captain (Flying Pilot); he chose to fly the localizer 18 approach into Denton. The glideslope portion of the ILS was out of service. We calculated landing performance as per Company procedures and verified it with the flying pilot. The performance data showed a 4;300 FT for a wet runway with a ref of 116 KIAS. Runway 18 at Denton is 7;000 FT. The approach was very normal and we broke out as the reported weather showed. Wind check from tower on a 2 mile final was from 080 at 19 KTS. Upon landing; we noted the runway was wet and later on noted small areas of standing water. The aircraft touched down on Ref (116 KTS). The brakes were applied; followed by the lift dump within the first 1;000 FT of the runway threshold. The lift dump felt to be operating correctly; but we immediately noticed the brakes did not seem normal and the Captain even commented that to me. I never felt the anti-skid system cycle at all throughout the entire landing. The Captain had control of the airplane and was able to maneuver as necessary. I started calling out runway distances when we had approximately 5;000 FT remaining.With approximately 2000 FT remaining; and feeling like we may not be able to stop; the Captain decided to shut down the right engine in order to remove excess thrust. He also called the tower to inform them that we would most likely be going off the end of the runway. With approximately 1;000 FT remaining; he turned off the anti-skid system as we both felt it was not functioning correctly. We then felt the tires grab and from there on he just made sure we were tracking perfectly straight with maximum braking effort; thinking we would be exiting the runway.I estimate we exited the runway at around 20 KTS. Once stopped; we made sure everyone was safe and sound. We then called the tower again to tell them we indeed had gone off the runway and had come to a stop about 60 FT off the end and everyone was safe. The Captain then directed me (type rated for a RA390); due to the fact that I'm an A&P mechanic; to do a walk around to get a general idea of the state of the aircraft before personnel arrived to disembark the passengers and begin to extract the aircraft. I noted that the left main tire was flat. As soon as all the passengers were safely on their way to the FBO; the Captain contacted our Director of Operations via cell phone.I am filing this report due to the FAA referring to this event as an incident when corresponding with us. To the best of my knowledge; and in consultation with our Director of Operations; this event does not fall under the category of an accident or incident as per the FARs definition. There was also no loss of separation or conflict between any aircraft. [Report narrative contained no additional information.] On landing rollout on a wet runway; flight crew experienced malfunction of aircraft's anti-skid system. As a result; the aircraft rolled off the end of the runway at low speed and experienced a blown tire. Passengers were evacuated and the aircraft was towed to the ramp.